Encryption Schemes based on a Single Permutation: PCBC, POFB, PCFB and PCTR

摘要

In this paper we discuss how to construct encryption schemes from permutations. Firstly we discuss an intuitive way to design permutation-based encryption schemes, that is by combining mainstream blockcipher-based encryption modes (such as CBC, OFB, CFB, CTR) with the Even-Mansour cipher, which is an elegant permutation-based blockcipher. Unfortunately, most of encryption schemes produced by the combination strategy are not secure enough. Then we propose 4 permutation-based encryption schemes - PCBC, POFB, PCFB and PCTR, which can resist both the blockwise adaptive attack and the Φ~{direct+}-related-key attack when using a non-repeated nonce. To illustrate it, we give a definition of the indistinguishability from random bits against blockwise adaptive chosen plaintext attack in the Φ~{direct+}-related-key setting, and then prove the security of PCBC in such definition. The other 3 schemes have similar results. Constructing from a single permutation, these 4 encryption schemes are practical, in the sense that they are less prone to misuse, bring less pressure on the key-management in real world, and apply to blockwise adaptive scenarios including real-time applications, on-line settings, memory-restricted devices, etc. Moreover they are more efficient than the Sponge construction.